# I Hurwitz Identity Proof

1. Jan 22, 2017

### binbagsss

Hi,

My notes say that hurwitz identity currently has no elementary proof?

One way to prove the identity is through modular forms: to consider Eisenstein series, $E_4^2$ and $E_8$ , note that the dimension of space of modular functions of weight 8 is one, find the constant of proportionality to be $1$ by comparing the first coefficient which is identically one (sufficing here since the dimension of the space is one) and so the identity comes out by setting these two Eisenstein series equal.

What other proofs are there?

Thanks

2. Feb 22, 2017